(a) The position vectors of points L and M are (5i + 6j) and (13i + 4j) respectively. If point K lies on LM such that LK : KM is 2 : 3, find the position ve...

(a) The position vectors of points L and M are (5i + 6j) and (13i + 4j) respectively. If point K lies on LM such that LK : KM is 2 : 3, find the position vector of K.

(b) Three poles are situated at points A, B and C on the same horizontal plane such that \(AB = (8km, 060°)\) and \(BC = (12km, 130°)\). Calculate, 

(i) |AC|, correct to three significant figures ; (ii) the bearing of C from A, correct to the nearest degree.